Stabilization of product states and excited-state quantum phase transitions in a coupled qubit-field system

We study a system of single qubit (or few qubits) interacting with soft-mode bosonic field. Considering an extended version the Rabi model both parity-conserving and parity-violating interactions, we disclose complex arrangement quantum phase transitions in ground- excited-state domains. An experimentally testable signature some these is dynamical stabilization fully factorized qubit-field state involving field vacuum. It happens ultrastrong coupling regime where superradiant equilibrium far from vacuum state. The degree varies abruptly interaction parameters increases softness mode. analyze semiclassical origins effects show their connection to various forms transitions.